# What does "H" mean?!

by jaja1990
Tags: None
 P: 26 I have this question in my assignment paper:- 8. Sketch the graph of: (a) y = |2x − 2|; (b) y = 2H(x − 4) (a) is obvious, but how do I sketch (b)? Does "H" stand for some specific constant?
 P: 708 Possibly, the Heaviside step function H(x) http://mathworld.wolfram.com/HeavisideStepFunction.html
 P: 26 The webpage in the link you've given says:- The function is:- 0 when x < 0, 1/2 when x = 0, 1 when x > 0. But here: http://simple.wikipedia.org/wiki/Heaviside_Function, defines the function as:- 1 when x => 0, 0 when x < 0. To begin with, which should I follow?
P: 708

## What does "H" mean?!

I think that H(0)=0 correponds to an old definition remaining from history and that the standard definition is with H(0)=1/2.
Generally this is of no consequence in partical applications.
P: 4,542
 Quote by JJacquelin I think that H(0)=0 correponds to an old definition remaining from history and that the standard definition is with H(0)=1/2. Generally this is of no consequence in partical applications.
If one wanted to use an approximation like a fourier series version, then it makes sense to define H(0) as 1/2 based on properties of fourier series when you have this kind of 'Gibbs' phenomenon.

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